Manual says select 1st and 4th with 4 synchro boxes, 2nd & 4th with 3 synchro ones.
Don't select 2nd and 3rd together, the torque multiplication between them will rip teeth off, as my mate found with his Sprite box.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

And don't use rattle guns

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Respect mine and I'll respect yours.

The Bushes for the gear lever shaft in the back of diff housing can be replaced by a Dufor Bush DB155 available from any reputable bearing outlet.

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DID I MENTION THAT I AM THE BEST SUPPLIER FOR MINI ELECTRICAL PARTS AND REPAIRS?
"Let us remove your "SHORTS"

Maybe. I've taken them off with a rattle gun before. If it's the first time the nuts have come off since the factory, they will be held on very hard. I had it upside down on the floor with my dad and brother standing on top, and it was still turning the box before the bolt would move.

I bolt a 2M length of conveyor side channel (150mm wide U section) to the top of mine and sit it on the ground. It ain't going anywhere..

I used to wind the boat trailer's bum down onto it, but thats in Qld now so I made other arrangements.
My mate bolts his on top of the sturdy workbench, that works too.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

I got it all apart, now I either need replacement gear parts or a complete replacement gear set. How do I tell what laygear I have if their is a difference?

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Respect mine and I'll respect yours.

There is a number on the laygear,
std gears use a 22G927, Cooper S and GT gears (with 18T 1st motion shaft) use a 22G1040.

If you need a 927 laygear you can have one for postage.

Good 2nd gears are hard to find, the engagement dogs get chewed up if/when the synchro goes.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

I ordered a used 2nd gear from Guessworks UK: http://www.guess-works.com/Shop/Parts/? ... %20Aseries

I think it was a bit cheaper when I got it, but still not the $100+ for a new one. They had re-surfaced the cone of the gear too, and it seemed to work well (didn't solve my 2nd gear cruchies, but I don't think the gear's to blame). If you can't find an equivalent Australian supplier, I would recommend Guessworks.

I'm doing a bit more work on this again.
What is the best way to remove the studs and locating pins from the housing

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Respect mine and I'll respect yours.

The studs all screw out, either use 2 nuts locked together or a pair of vicegrips.

The dowels come out with multigrips if stuck in the housing. If tight, warm the case there with a hot air gun.
Then deburr the dowels by holding in a drill and using sandpaper, if necessary.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

I never did - but if I were to try, I'd use vise-grips with something soft in the jaws (maybe gasket cork?) to avoid damaging them.

If you do take them out, it would be a good idea to re-tap the threads just to remove crud; after cleaning anything can get in there.

Edit - the doc beat me to it!